Here's the spreadsheet which Randall used to calculate the times and dates for the comic. It also has a lot of other percentages and dates, so take a look if you are interested.

Cueball/Randall creates this formula which helps him wait for long stretches of time which goes increasingly faster into the past as more time goes by, which gives him the effect of looking like the time goes by quickly. Which assists in the waiting process.

As far as the actual math is concerned, the formula is an exponential function (i.e. the variable appears in the exponent). The effect that the function grows faster and faster as p grows, is due to T(p) being exponential. More precisely, when you repeatedly add some constant to the exponent, you will repeatedly multiply some (other) constant with the value of the function. Compare how "slow" a value grows by adding even high values (1, 1001, 2001, 3001, 4001, 5001…) and how fast it grows by multiplying even low values (1, 10, 100, 1000, 10000, 100000…)

Now, the function has to be adjusted so that, as Randall put it, "the time spent in each part of the past is loosely proportional to how well I know it." The most important adjustment is putting p to the power of three. That lowers the amount added to the exponent for low values (0.1³=0.001, 0.2³=0.008, i.e. only 7/1000 have been added for 10% workflow) and increases the amount for high values (0.8³=0.512, 0.9³=0.729, i.e. more than 1/5 has been added for 10% workflow). That means the recent past will pass even slower and the historic past even faster than it already does by choosing an exponential function.
The remaining adjustments are technical. The coefficient in front of p³ adjusts the constant by which the result will be multiplied while adding some constant to p, while it also roughly ensures that p=1 yields the lifetime of the universe. The 3 added to the product in the exponent further adjusts the actual values of the power without touching the slope (the multiplicative constant). In the parentheses, e³ is subtracted to put the time to 0 when p=0. Otherwise the function would start approx. 20 yrs and 1 month ago. For bigger p, this offset does not matter much. Imagine subtracting 20 yrs from the lifetime of the universe!

Finally, the result is subtracted from the current date for aesthetical reasons. The formula could tell you "20 yrs ago", or it could read "February 1992". Randall decided the latter would be better.

The punchline "Swoosh!" is about how fast the last few percents of Cueball's download happen in "such a rush". For most humans waiting for a download to complete tends to become really boring and progress would instead seem to get slower and slower.

It moves slowly through the first few years, then steadily accelerates. I tuned the formula so the time spent in each part of the past is loosely proportional to how well I know it. This means I hit familiar landmarks with each bit of progress, giving me a satisfying sense of movement.

[The following are panels detailing completion percentages, correlated time periods, and notable events from this time period.]

7.308% December 18, 2011

Around this time:

Kim Jong-Il dies. US leaves Iraq.

31.12% February 1995

Around this time:

Windows 95 debuts. OJ found not guilty.

47.91% 1844

Around this time:

Rubber vulcanized, bicycle invented, wrench patented.

70.33% 24,000 years ago

Around this time:

Caves painted, ceramic art made. Neanderthals extinct.

90.42% 68 million years ago

Around this time:

First flowering plants. Chicxulub impact kills off most dinosaurs.

100% 13.76 billion years ago

Around this time:

Universe begins. First stars ignite.

Download complete.

[Cueball watches a download progress on a laptop in amazement and happiness. Megan stands nearby and looks at Cueball with a bemused posture.]

I find it more aesthetically pleasing to have the time running forwards; starting with the big bang and ending in the present day. Which reminds me strongly of the introduction to the Big Bang Theory series. Popup (talk) 09:27, 28 June 2013 (UTC)

I am not sure, but it looks like Randall acted up the inverse. It has no reference to the current date, and I am not sure, but I think it should be a cube root. 72.70.180.234 19:39, 21 October 2013 (UTC)

It does indeed reference the current date. Note the T in ln(T... --141.101.98.63 03:58, 27 April 2016 (UTC)

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